Life TablesAgenMx nqx npxlx ndx nLxTxex0 8.05229 0.00802 0.99198 100,000 802 99439 7302192 73.021 0.41785 0.00167 0.99833 99,198 166 396460 7202753 72.615 0.22212 0.00111 0.99889 99,032 110 494885 6806293 68.7310 0.28420 0.00142 0.99858 98,922 140 494260 6311408 63.8015 1.10706 0.00552 0.99448 98,782 545 492548 5817148 58.8920 1.51572 0.00755 0.99245 98,237 742 489330 5324600 54.2025 1.55401 0.00774 0.99226 97,495 755 485588 4835270 49.6030 1.99793 0.00994 0.99006 96,740 962 481295 4349682 44.9635 2.57852 0.01281 0.98719 95,778 1227 475823 3868387 40.3940 3.45763 0.01714 0.98286 94,551 1621 468703 3392564 35.8845 4.75179 0.02348 0.97652 92,930 2182 459195 2923861 31.4650 7.05218 0.03465 0.96535 90,748 3144 445880 2464666 27.1655 10.83790 0.05276 0.94724 87,604 4622 426465 2018786 23.0460 17.52564 0.08395 0.91605 82,982 6966 397495 1592321 19.1965 25.99643 0.12205 0.87795 76,016 9278 356885 1194826 15.7270 40.17717 0.18255 0.81745 66,738 12183 303233 837941 12.5675 59.60107 0.25936 0.74064 54,555 14149 237403 534708 9.8080 94.60571 0.38255 0.61745 40,406 15457 163388 297305 7.3685+ 186.30196 1.00000 0.00000 24,949 24949 133917 133917 5.37Construction of nLx – the role of nax11) Simple assumptionsa. .3-.7 weights for x=0b. equal distribution of deaths across other x-x+n intervals2) Use observed data3) Use models – parametric functions4) Borrow from other populations5) Borrow from model life tables2Open ended interval – x-1) How do we calculate Lx when we don’t know ax?2) Use formula for mxa.xxxxxxmdL,Ldm - we know both d and m3) Why do we typically stop life tables at age 80 (orlower)?3Life table rates1) What is the crude death rate for the life table?2) What is the crude birth rate?3) What is the life expectancy associated with a CDR of 50?4Remaining life expectancy1) What is the remaining life expectancy of US male who survives to age 65?2) Why is the life expectancy of a 65 year old longer than life expectancy at birth?3) How many years of life are US men expected to live between the ages of 20 and 65?4) What would life expectancy be if we eliminated childhood and adolescent (age 0-20) mortality?5Survival probabilities1) What is the probability of surviving to adulthood (i.e., 20th birthday)?a. l20/l0 b. =98% in US 1996 table and 67% in Afghanistan 1997 table2) What is the probability of surviving to your 65th birthday 65? 3) What is the probability of surviving to age 65 conditional on survival to age 20? {note, you cannot do this with an abridged life table}4) What proportion of you (men) would be alive in 30 years if you followed this life table?6Death probabilities1) What is the probability of dying during your 20s (i.e., between exact age 20 and exact age 30)? 2) What is the probability of between age 60 and age 80?7What is the median age at death?1) Find age groups bounding lx= ½l0 2) In US male table, between 75 and 793)n*llllxa5xnxn021xn4) In example, 6.765*406,40555,54000,05555,5475a 8Counterfactuals and decomposition1) What would U.S. life expectancy be if infant mortality was reduced to Swedish level?2) What would U.S. life expectancy be if racial disparities in infant mortality were eliminated?3) How much did decline in IMR contribute to increase in life expectancy?4) How much did decline in old age mortality contribute toincrease in life expectancy?9Decomposition2nx1nx101x102nx1x1xn2x2xn101xxnllll*lTlLlL*llΔComponentsxnΔ=change/difference in life expectancy between x-n101xll=prob of surviving to age x in time/pop 12x2xnlL = avg. number of person-years lived between x-n2x1xll=relative likelihood of survival to age x in two pops102nxlT=avg number of years lived beyond age x in new regime10Review – Problem set #61) Calculation of mean agea. What is the mid-point of the 15-19 age interval?2) Remember how to calculate median agea. Beginning of age interval plusb. Proportion of age interval until middle obs.3) SMAMa. Role of prop. never married at 50-54 11Mean age at marriage – PS6Age Midpoint Men Women Sum Sum15-19 17.5 1,284 7,014 22470 12274520-24 22.5 11,008 15,716 247680 35361025-29 27.5 16,273 11,135 447507.5 306212.530-34 32.5 6,106 2,870 198445 9327535-39 37.5 1,940 956 72750 3585040-44 42.5 897 463 38122.5 19677.545-49 47.5 937 291 44507.5 13822.538,445 38,445 1071483 945192.527.87053 24.58558Median age at marriagel=25 for men, 20 for womenmiddle marriage =38,445/2=19,222Years from beginning of middle age group:=(19222-12292)*(5/16273)=2.129 for men=(19222-7014)*(5/15716)=3.884 for